The dynamic behaviour of pipelines in stinger and J-type pipelaying is studied by solving numerically a three-dimensional, nonlinear, large deformation model. The pipeline is modeled as a thin-walled, slender, locally stiff, extensible or inextensible, tubular beam-column, subject to nonlinear, three-dimensional, deformation dependent hydrodynamic loads, torsion, distributed moments, varying axial tension, internal and external fluid static forces, gravity, and seabed friction. Unilaterial contact constraints are imposed by the fixed seabed and the moving stinger. A time incremental, finite element algorithm is developed to solve the problem numerically by gradually applying the load. Nonpenetration and nonadhesion principles are used to impose the seabed and the time dependent stinger constraints. Constrained degress of freedom are identified and assembled in a condensed problem, which produces constraint reaction forces. In order to study the pipelaying dynamics, several applications are simulated numerically for two and three-dimensional, moderate and deep water, stinger and J -type pipelaying.